In garments we rip along the line at which they were sewed; we tear the texture of the cloth. ... Rend implies great force or violence. [Century Dictionary]

Meaning "to move with slashing force" (1798) is the sense in let her rip, American English colloquial phrase attested from 1853. The noun is attested from 1711. The parachutist's rip cord (1911) originally was a device in ballooning to open a panel and release air.

n.1

"rough water," 1775, perhaps a special use of rip (v.). Originally of seas; application to rivers is from 1828.